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Nonparametric graphon estimation

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arxiv 1309.5936 v1 pith:56FGKKZY submitted 2013-09-23 math.ST math.COmath.PRstat.TH

Patrick J. Wolfe , Sofia C. Olhede This is my paper
classification math.STmath.COmath.PRstat.TH
keywords estimationgraphonnonparametricnetworksresultssparsetheoryunder
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We propose a nonparametric framework for the analysis of networks, based on a natural limit object termed a graphon. We prove consistency of graphon estimation under general conditions, giving rates which include the important practical setting of sparse networks. Our results cover dense and sparse stochastic blockmodels with a growing number of classes, under model misspecification. We use profile likelihood methods, and connect our results to approximation theory, nonparametric function estimation, and the theory of graph limits.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Distance-Preserving Embeddings in Inhomogeneous Random Graphs

    cs.LG 2026-07 accept novelty 7.0 of 10

    On supercritical inhomogeneous random graphs, multi-scale landmark embeddings achieve (1±ε)-distortion of shortest paths at dimension Ω(n^{1-ε} log n), far below worst-case, with universal kernel extensions and transf...

  2. Bias-Corrected Multiplier Bootstrap Inference for Spectral Edges of Large Covariance Matrices

    stat.ME 2026-07 conditional novelty 7.0 of 10

    A calibrated multiplier bootstrap regularizes bulk-edge eigenvalues to a Gaussian scale, bias-corrects the induced edge shift, and produces valid edge CIs plus a spike-count estimator.

  3. Decorated graphons for temporal network estimation

    stat.ME 2026-07 conditional novelty 6.0 of 10

    Dynamic networks can be modeled as decorated graphons whose edge labels are binary time-series laws, estimated by two-stage blockwise least squares with rates depending on the number of time steps and edge-estimator quality.

  4. A Spectral Framework for Graph Neural Operators: Convergence Guarantees and Tradeoffs

    stat.ML 2025-10 conditional novelty 2.0 of 10

    Three existing graphon sampling bounds give GNN eigenvalue-convergence rates of (log n)^-1/4, sqrt(log n/n), and (log n/n)^1/4; the note unifies and tests them, finding all loose.

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